I recently went out of my way to mention that Aerolíneas has had nicer service lately - two days later, I hear about a flight that has most lights in the plane (passengers' seat lights) not turning on, except for a handful that didn't turn off the whole flight...
Then again, American has a daily evening flight from New York down here - 3 times during the past week the flight was delayed 10 hours, departing the next morning. So pick your poison, I guess...
Ultimately American is integrated with far more airlines and thus offers more options than Aerolíneas - even in Latin America, and certainly throughout the world.
Safety-wise, they both have great records.